Ever since the childhood of electrical engineering, it has been a desire to be able to detect the type of fault described above. Consequently, there are a large number of different principles for solving the technical problem. One of the reasons for this is that the neutral point of the networks in relation to ground is treated in different ways. Keeping pace with the general technical development, the technical solutions to this problem have also undergone great changes. Previous classical, analog solution principles have nowadays given way to more or less sophisticated solutions based on computer technique, approximation of measured signal values to mathematical functions, estimation of parameters included, numerical technique and statistical methods.
The state of the art will therefore be described on the basis of the protection devices which have been developed during the last few years, based on computer technique.
It is self-evident that it is desired to be able to detect as great high resistance ground faults as possible. By pure definition, the limit to what may be considered a high resistance fault seems to be somewhat vague. This is a consequence partly of the limits that are detectable in practice and partly of the additional requirements which are often placed on these protection devices. In addition to the desire to detect a high resistance fault, it is also desired to know in what direction a fault is located in relation to an outgoing measuring station and, if possible, the distance to the site of the fault.
The types of faults described above often give rise to ground fault resistances of the order of magnitude of 5-10 k .OMEGA.. However, in IEEE Proceedings, Vol. 130, pt. C, No. 6, November 1983, page 306, in an article entitled "Microprocessor-Based Algorithm for High-Resistance Earth-Fault Distance Protection", Yang, Morrison and Eng state that a maximally allowed upper limit to a ground fault is 200 .OMEGA. if it is also desired to determine the distance to the fault.
In an article entitled "A Microprossor-Based Technique for Detection of High Impedance Faults" by Balser, Clements and Lawrence, published in IEEE Trans. on PWRD, Vol. PWRD-1, No. 3, July 1986, it is stated, however, that a fault representing a considerably higher resistance can be discovered. This indicates that it should be simpler to discover a fault but that it is problematic to find a model which enables the determination of the distance to the fault.
For a protection device that is intended to react to low-ohmic faults, the problem of protection can be approached from essentially two different points of view. From the first one a physical model of the system to be protected is used. This can be set up by applying Kirchhoff's laws. This leads to a relation between the different currents and voltages in the form of impedance and admittance matrices for the system. In an article by Thorp, Phadke, Horowitz and Beehler entitled "Limits to Impedance Relaying", published in IEEE Trans. on PAS, Vol. PAS-98, No. 1, Jan/Feb 1979, pp. 240-60, it has been described, however, that there are considerable limitations to structures which are based on impedance models.
In the second model, knowledge of the structure of the signals in the system is used to adapt some function to the measured values. This can be carried out by approximating the signal with a combination of mathematical functions. In, for example, an article entitled "A New Filtering Based Digital Distance Relay" by Girgis, published in IEEE Trans. on PAS, Vol. PAS-101, No. 9, September 1982, pp. 3471-80 and in an article entitled "Fundamental Bases for Distance Relaying with Symmetrical Components" by Phadke, Ibrahim and Hlibka in IEEE Trans. on PAS, Vol. PAS-96, No. 92, March/April 1977, pp. 635, 46, each individual signal is represented by truncated Fourier series. When successively measured values exist, the coefficients of the signal can be estimated by applying recursive algorithms. However, when the fault impedance has a large amount, problems may arise in discovering the differences between the different phase quantities. This is mostly due to the limited resolution in the implementation with a limited word length. Owing to this fact, there are advantages in estimating the Fourier components for a suitable combination of the current quantities instead of the individual phase quantities.
Protection devices which are designed to operate when high resistance ground faults arise are patented in several different designs. Most conventional methods which are used in existing patents for high resistance ground faults are based on impedance models for the transmission line. This may be a doubtful philosophy of approach since impedance for sinusoidal signals is really only defined for stationary phenomena. During the transient stage after a fault, on the other hand, the information is limited and it may therefore be difficult to carry out the analysis in the impedance plane. The measurement errors which arise in high resistance ground faults are therefore particularly pronounced. The disadvantages of the impedance plane analysis have been described by Phadke, Ibrahim and Hlibka in the article cited above.
One way of avoiding the problems mentioned above has been investigated by analog implementation in the U.S. Pat. No. 4,352,137 entitled "Method and Device for Fault Detection", which describes a method which is based on utilizing the propagation of travelling waves over the transmission line. Such algorithms manage to treat the transient phenomena but must be complemented with conventional distance and overcurrent relays to be able to be applied during stationary conditions. The effectiveness of the concept thus obtained has proved to be considerably higher than in corresponding impedance methods. However, since the method is, in principle, a transient-sensing method, it may be hazardous to base a decision about extremely great high resistance faults on this method.
British Pat. No. 2012505 entitled "Protective Relaying Apparatus" and U.S. Pat. No. 3,963,964 entitled "Phase Comparison Relay for Protecting a Line Section of a Multi-Phase Power Transmission Network" describe protective devices for high resistance ground faults which are based on a comparison of the phases at the two end points of a protected section of a transmission line.
U.S. Pat. No. 4,091,433 entitled "Protective Relay Circuit for Interphase Faults" describes a device based on the study of symmetrical components instead of on the phase quantities themselves.
U.S. Pat. No. 3,614,534 entitled "Electrical Protective Systems" and Canadian Pat. No. 946,928 entitled "Ground Fault Detector and Circuit Interrupter by Magnetic Flux Storage Method" describe devices in which the error signals are stored in the form of a magnetic flux in an inducing core. The described method seems to operate satisfactorily for a fault resistance of the order of magnitude of 2 k .OMEGA..
As is clear from the above, quite a large number of patents have been granted for devices which are intended to discover high resistance ground faults. However, most of them are impedancebased and/or have a discriminating portion which has been implemented using analog technique. In other respects, the standards for how high fault resistance that can be managed have changed over the years. It is of the utmost interest to be able to handle as high fault resistances as possible. For this purpose, new methods are required, above all when it comes to the analyzing part of the relay unit.
A description of the state of the art as regards protection for high resistance faults cannot necessarily be considered complete without briefly mentioning two major long-term research projects in the USA, dealing with high impedance ground faults. One of the projects is being carried on at Texas A&M University by order of The Electric Power Institute. An account of this project work is published in IEEE Trans. on power Apparatus and Systems, Vol. PAS-101, No. 6, June 1982, pp. 1596-606 and is entitled "Distribution High Impedance Fault Detection Utilizing High Frequency Current Components", written by Aucoin and Russel. This projects has been going on for many years and the object has been to investigate the properties of real high impedance fault. Analyses have been made of data gathered from faulted conductors. The detection logic is based on analyzing the energy which is present in frequency components of the current of a higher order. To this end, FFT analysis is applied to obtain the properties of the studied signals from the distribution line. In this connection, individual peaks representing noise are disregarded, and the main interst is concentrated on indicating the cumulative effect of many such peaks during a short period of time.
Extensive investigations have been carried out through offline simulation of collected data. A prototype has also been produced for verifying the methods used in real time. This is based on data being collected with a frequency of 2-10 kHz during one period. These data are then processed with the algorithm which has been produced by simulation studies.
The second project is being conducted at The Electric Power Institute as an independent work. Also in this case extensive analyses of collected data from distribution lines in the field have been performed. It has been found that high resistance faults can be classified into two groups, namely, passive and active. The former originates from such situations where a conductor has broken and thus causes an unbalance in the current which is measured at a substation. The latter type of fault arises when a conductor comes into contact with conducting material and arcing arises. In this case the unbalance occurs not only in the basic component but also in the different harmonic components and primarily in the odd harmonics. The detection algorithm is thus based on first calculating the Fourier coefficients for the 1st, 3rd and 5th harmonic phase currents. Thereafter, normalized sequence currents for each harmonic component are calculated. The covariance matrix for the estimations and a statistical test quantity are produced as a basis for the logic handling. In this method, a matrix of the same order of magnitude as the number of estimated parameters is updated. In addition, it is necessary to invert the covariance matrix. These are time-demanding procedures as far as the CPU is concerned, which has a negative effect on the highest sampling frequency that may be selected. In the present situation, therefore, no economically realistic implementation of this algorithm exists.
A very important and integral part of the invention which will now be described is that a concept, which is described in detail in U.S. patent application 212,225 entitled "Frequency relay", can also be used, after extension, in a protection device for high impedance faults. The concept according to the aforementioned U.S. application comprises converting a measured signal, obtained from the network, after filtering and digitization, into an analytical model in the form of a truncated Fourier series, the coefficients of which are determined in a parameter estimator operating with an estimation method in accordance with the least squares method. Starting from model values, according to the concept, calculation of the frequency can be carried out in a frequency estimator, whose output signal, on the one hand, is returned as current frequency value to the parameter estimator and, on the other hand, is a measure of the current frequency, for example for determining the limits to permissible frequency variations.
Since the parameter estimation technique is an important and integral part of the invention and since concepts from this technique will be used to describe the invention, a brief summary thereof, based on the technique as described in U.S. patent application 212,225, will be given. Current signals can be modelled by: ##EQU1## which can be transformed to EQU y(t)=.theta..sup.T .psi.(t) (2)
where EQU .theta..sup.T =(a.sub.0, -a.sub.0 b.sub.0, c.sub.1 cos d.sub.1, c.sub.1 sin d.sub.1, . . . c.sub.N cos d.sub.N, c.sub.N sin d.sub.N) (3)
is a parameter estimation vector and EQU .psi.(t)=(1, t, sin .omega..sub.0 t, cos .omega..sub.0 t, . . . sin N .omega..sub.0 t, cos N .omega..sub.0 t) (4)
is a regressive vector.
Estimation of the parameters according to the least squares method means that the value of a "loss function" V.sub.N is minimized.
This loss function is a measure of the energy of the deviation between actual signal and model signal during an exponential time window backwards from the current point in time t. The contribution to the loss function of the previous instantaneous model deviations of the signal is controlled with the foregetting of the interval .lambda., which is usually selected in the interval 0.9 to 1.0. Thus, the least squares adaptation aims at minimizing the deviation, which is the same as selecting an adequate model order. V.sub.N can be written as ##EQU2## where .lambda. is a forgetting factor and where .epsilon.(t) is an estimation error function.
The minimization gives the following equation for .theta.(t) ##EQU3##
The actual estimation is performed recursively with the aid of the following algorithm ##EQU4## Here, R(t) is the covariance matrix of the regression vector and P(t), as shown below, is the inverse thereof. Otherwise, the following recurrence formulas will be used: ##EQU5## Another concept, also belonging to the prior art, will be used with the invention now described. For reasons which will be given later on, modal transformations will be applied. Such transformations are described, inter alia, in Proceedings IEEE 113, June 1966, in an article entitled "Study of symmetrical and related components through the theory of linear vector spaces", as well as in the U.S. Pat. No. 4,719,580 entitled "Line protection". In the present invention the possibilities of transforming phase signals to corresponding symmetrical components by an orthogonal transformation matrix are utilized.
The object of the invention is to provide a more sensitive protection device for extremely high resistance faults than what is possible to achieve using the present technique. In this connection it is an important desire that a tripping signal should not be delivered for unbalanced load currents which originate from unsymmetrical loads. In addition to the protection device being transient sensing, therefore, the invention also comprises a method whereby stationary states are taken into consideration by carrying out static analysis. To this are to be added the usual advantages of numerical technique as compared with pure analog implementation of the relay concept.